Solving 3rd Order Dynamical Systems

In summary, the conversation discusses the use of pplane6 in evaluating second-order systems in MATLAB and the limitations of the software in handling higher-order systems. The speaker also mentions the need for a program that can analyze and graphically interpret third-order systems and suggests writing a custom codec in MATLAB as a solution.
  • #1
abercrombiems02
114
0
often in my differentail equations class i took last semester we frequently evaluated 2nd order systems, they could easily be calculuted in MATLAB using pplane6, however pplane6 can only solve systems of 2nd order or less, because as its name says its a phase plane, meaning it can only evaluate the relationship between two variables simultaneously. Often in my dynamics class i find that I need to evaluate 3 states when working in three dimensions and always have to choose a numerical value for one of my variables and then evaluate the phase plane at that point, does anyone out there know of any software that can analyze and graphically interperet a 3rd order system of higher?
 
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  • #2
I know that what I am going to say to you is not going to like you too much. But if you want to learn more, write your own codec in Matlab. Your class companions will treat you with a lot of respect. :rofl:

This is said by someone tired of searching Matlab programes in internet. I never found what I am looking for (Hey! it sounds to me as a U2 song).
 
  • #3


There are several software options that can solve and graphically interpret 3rd order dynamical systems. Some popular choices include Maple, Mathematica, and MATLAB's Control System Toolbox. These programs have built-in functions and tools specifically designed for solving higher order systems of differential equations. Additionally, there are also online resources and tutorials available for using these software programs to solve 3rd order dynamical systems. It may also be helpful to consult with your professor or classmates for recommendations on which software would be best suited for your specific needs.
 

What is a 3rd order dynamical system?

A 3rd order dynamical system is a mathematical model that describes the behavior of a system over time, based on three variables or dimensions. It is a type of differential equation that represents how the system's state changes over time.

What are the steps to solve a 3rd order dynamical system?

The steps to solve a 3rd order dynamical system are as follows: 1) Set up the differential equation by identifying the three variables and their relationships. 2) Find the general solution by solving the differential equation using integration. 3) Use initial conditions to find the specific solution for the system. 4) Plot the solution to visualize the behavior of the system over time.

Can 3rd order dynamical systems be solved analytically?

Yes, 3rd order dynamical systems can be solved analytically using mathematical techniques such as integration and substitution. However, in some cases, the solution may be too complex to find analytically and numerical methods may be used instead.

What are the applications of solving 3rd order dynamical systems?

Solving 3rd order dynamical systems has many practical applications in various fields such as physics, engineering, biology, and economics. It can be used to model and predict the behavior of complex systems, design control systems, and understand natural phenomena.

What are some common challenges when solving 3rd order dynamical systems?

Solving 3rd order dynamical systems can be challenging due to their complex nature and the need for advanced mathematical techniques. It may also be difficult to find an analytical solution in some cases, requiring the use of numerical methods. Additionally, accurately defining initial conditions and parameters for the system can be crucial in obtaining an accurate solution.

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